The energy stored in the electric field produced by a metal sphere is 4.5 J. If the sphere contains 4 μ C charge, its radius will be: [Take: (1/4 π ϵo ) = 9 × 109 N - m2 / C2 ]

Question

The energy stored in the electric field produced by a metal sphere is 4.5 J. If the sphere contains 4 μ C charge, its radius will be: [Take: (1/4 π ϵo ) = 9 × 109 N - m2 / C2 ] (A) 20 mm (B) 32 mm (C) 28 mm (D) 16 mm

Tardigrade Admin · Accepted Answer

Energy of sphere = (Q2/2C) 4.5 = (16×10-12/2C) C = (16×10-12/9) = 4πε0R R = (16×10-12/9)×(1/4πε0) = 9×109×(16/9)×10-12 = 16 Ã 10-3 = 16 mm

Q. The energy stored in the electric field produced by a metal sphere is $4.5 J$ . If the sphere contains $4 μ C$ charge, its radius will be : [Take : $\frac{1}{4 π ϵ _{o}} = 9 \times 1 0^{9} N - m^{2} / C^{2}$ ]

20 mm

32 mm

28 mm

16 mm

Energy of sphere = $\frac{Q ^{2}}{2 C}$
$4.5 = \frac{16 \times 1 0 ^{- 12}}{2 C}$
$C = \frac{16 \times 1 0 ^{- 12}}{9} = 4 π ε_{0} R$
$R = \frac{16 \times 1 0 ^{- 12}}{9} \times \frac{1}{4 π ε _{0}}$
$= 9 \times 1 0^{9} \times \frac{16}{9} \times 1 0^{- 12}$
$= 16 \times 1 0^{- 3} = 16 mm$

Q. The energy stored in the electric field produced by a metal sphere is 4.5J. If the sphere contains 4μC charge, its radius will be : [Take : 4πϵo​1​=9×109N−m2/C2 ]